First-Principles Study of Magnetoelectric Coupling at $\mathrm{Fe}/\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3(001)$ Interfaces

We predict strong interface multiferroicity at $\mathrm{bcc}\text{−}\mathrm{Fe}/\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3(001)$ heterointerfaces by using first-principles calculations. For the identified stable atomic structure, we quantify the changes in the orientation of the magnetic moments of bcc $\mathrm{Fe}$ due to the reversal of the electric polarization of $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$. By determining the magnetoelectric tensor, we find that the magnetoelectric coupling of the present ferromagnetic-multiferroic interface is an order of magnitude larger than that of a ferromagnetic-ferroelectric interface, $\mathrm{bcc}\text{−}\mathrm{Fe}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3(001)$.

Figure 1

Initial structures of the $\mathrm{Fe}/\mathrm{BFO}(001)$ heterointerfaces: side views of the UP structures for (a) the ${\mathrm{B}}^{\mathrm{O}}$ and (b) ${\mathrm{F}}^{\mathrm{O}}$ systems; top views of (c) the ${\mathrm{B}}^{\mathrm{O}}$, (d) ${\mathrm{B}}^{\mathrm{B}}$, (e) ${\mathrm{F}}^{\mathrm{O}}$, and (f) ${\mathrm{F}}^{\mathrm{B}}$ systems. See the text for the definition of the structure indexes. Solid and dashed lines indicate unit cells of $\mathrm{BFO}(001)p\left(\sqrt{2}\times \sqrt{2}\right)R{45}^{\circ }$ and of bcc $\mathrm{Fe}(001)$, respectively.

Figure 2

(a) Total energy differences $\mathrm{\Delta }{E}_1$ between the systems in which bcc-$\mathrm{Fe}$ atoms are stacked on the ontop and bridge sites of the BFO(001) atoms, defined as $\mathrm{\Delta }{E}_1=E_{\mathrm{ontop}}-E_{\mathrm{bridge}}$. (b) Interface energies $E_{\mathrm{int}}$ defined as in Eq. (1) for the ${\mathrm{B}}^{\mathrm{B}}$ and ${\mathrm{F}}^{\mathrm{B}}$ systems. (c) The optimized atomic positions of the UP and the DOWN structures for the ${\mathrm{B}}^{\mathrm{B}}$ system.

Figure 3

The MAE per bcc-$\mathrm{Fe}$ atom for each bcc-$\mathrm{Fe}$ layer.

Figure 4

Schematic presentation of magnetization vectors of BFO and bcc $\mathrm{Fe}$ in the vicinity of the interface for (a) UP and (b) DOWN structures.

Figure 5

The PDOS for the $d_{x^2-y^2}$ orbital of (a) the $\mathrm{Fe}1$ and (b) $\mathrm{Fe}2$ atoms for bulk BFO and for each $\mathrm{Fe}{\mathrm{O}}_2$ layer in the UP structure.